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Studying the strongly coupled N=4 plasma using AdS/CFT

Studying the strongly coupled N=4 plasma using AdS/CFT. Amos Yarom, Munich. Together with S. Gubser and S. Pufu. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A A. AdS/CFT. J. Maldacena. Calculating the stress-energy tensor. T .

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Studying the strongly coupled N=4 plasma using AdS/CFT

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  1. Studying the strongly coupled N=4 plasma using AdS/CFT Amos Yarom, Munich Together with S. Gubser and S. Pufu TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAA

  2. AdS/CFT J. Maldacena Calculating the stress-energy tensor T >> 1 N >> 1

  3. Calculating the stress-energy tensor • Anti-de-Sitter space. • Strings in Anti-de-Sitter space. • The energy momentum tensor via AdS/CFT. • Results.

  4. ds2 dz2 dy2 dx2 Flat space + dw2 ds2 dx2 dy2 + dz2 - dt2 ds2 = c2 dx2+c2 dy2+c2 dz2 = + y x  c x y  c y z  c z x z

  5. + 5d Anti de-Sitter space ds2 =L2 z-2 (dz2+dx2+dy2+dw2 - dt2) 0 z

  6. AdS5 black hole ds2 =L2 z-2 (dz2/(1-(z/z0)4)+dx2+dy2+dw2 - (1-(z/z0)4) dt2) ds2 = gdxdx 0 z0 z

  7. 1 ___ 20 z0 z Strings in AdS ds2 = gdxdx ______ √g ( X)2 dd SNG= s X() X(,t) 

  8. AdS5 CFT AdS/CFT J. Maldacena N=4 SYM plasma via AdS/CFT Vacuum Empty AdS5 gYM2 N L4/’2 L3/2 G5 N2 J. Maldacena hep-th/9711200

  9. AdS5 CFT T>0 N=4 SYM plasma via AdS/CFT Empty AdS5 Thermal state Vacuum AdS5 BH gYM2 N L4/’2 L3/2 G5 N2 Horizon radius Temperature J. Maldacena hep-th/9711200 E. Witten hep-th/9802150

  10. AdS5 CFT z0 AdS/CFT Endpoint of an open string on the boundary SNG Massive particle =0 J. Maldacena X J. Maldacena hep-th/9803002 Static ‘quarks’ using AdS/CFT 0 ? z

  11. AdS5 CFT z0 Endpoint of an open string on the boundary SNG Massive particle =0 X J. Maldacena hep-th/9803002 Moving ‘quarks’ using AdS/CFT 0 ? z

  12. AdS5 CFT z0 Endpoint of an open string on the boundary SNG Massive particle =0 X J. Maldacena hep-th/9803002 Moving ‘quarks’ using AdS/CFT 0 z

  13. AdS5 CFT z0 Extracting the stress-energy tensor using AdS/CFT 0 gmn|b <Tmn> E. Witten hep-th/9802150 z

  14. 0 AdS5 CFT z0 z Metric fluctuations AdS black hole Extracting the stress-energy tensor using AdS/CFT gmn|b <Tmn> E. Witten hep-th/9802150 ds2 = gdx dx g = gAdS-BH+h

  15. z0 The energy momentum tensor (Friess, Gubser, Michalogiorgakis, Pufu, hep-th/0607022) 0 g=gAdS+ h z

  16. Energy density for v=3/4 (Gubser, Pufu, AY, ArXiv: 0706.0213, Chesler, Yaffe, ArXiv: 0706.0368) Over energy Under energy

  17. v=0.75 v=0.58 v=0.25

  18. Small momentum approximations (Friess, Gubser, Michalogiorgakis, Pufu, hep-th/0607022)

  19. Small momentum approximations (Gubser, Pufu, AY, ArXiv: 0706.0213) 1-3v2 < 0 (supersonic) 1-3v2 > 0 (subsonic)

  20. Small momentum approximations (Gubser, Pufu, AY, ArXiv: 0706.0213)

  21. Small momentum approximations (Gubser, Pufu, AY, ArXiv: 0706.0213) s=1/3 cs2=1/3

  22. Energy density for v=3/4

  23. 0

  24. v=0.75 v=0.58 v=0.25

  25. Large momentum approximations (Gubser, Pufu hep-th: 0703090 AY, hep-th: 0703095)

  26. Large momentum approximations (Gubser, Pufu hep-th: 0703090 AY, hep-th: 0703095)

  27. The Poynting vector (Gubser, Pufu, AY, ArXiv: 0706.4307) S? S1 V=0.25 V=0.58 V=0.75

  28. Sound Waves ? Small momentum asymptotics (Gubser, Pufu, AY, ArXiv: 0706.4307)

  29. Small momentum asymptotics (Gubser, Pufu, AY, ArXiv: 0706.4307)

  30. The poynting vector (Gubser, Pufu, AY, ArXiv: 0706.4307) S1 S? V=0.25 V=0.58 V=0.75

  31. Energy analysis (Friess, Gubser, Michalogiorgakis, Pufu, hep-th/0607022, Gubser, Pufu, AY, ArXiv: 0706.0213, 0706.4307)

  32. z0 0 z Energy analysis (Friess, Gubser, Michalogiorgakis, Pufu, hep-th/0607022, Gubser, Pufu, AY, ArXiv: 0706.0213, 0706.4307) F (Herzog, Karch, Kovtun, Kozcaz, Yaffe, hep-th: 0605158, Gubser, hep-th: 0605182)

  33. Energy analysis (Friess, Gubser, Michalogiorgakis, Pufu, hep-th/0607022, Gubser, Pufu, AY, ArXiv: 0706.0213, 0706.4307)

  34. Energy analysis (Friess, Gubser, Michalogiorgakis, Pufu, hep-th/0607022, Gubser, Pufu, AY, ArXiv: 0706.0213, 0706.4307) S1

  35. Summary • AdS/CFT enables us to obtain the energy momentum tensor of the plasma at all scales. • A sonic boom and wake exist. • The ratio of energy going into sound to energy going into the wake is 1+v2:-1.

  36. The energy momentum tensor Cylindrical symmetry Gauge choice Vector modes Tensor modes

  37. The energy momentum tensor Tensor modes Vector modes + first order constraint

  38. The energy momentum tensor Tensor modes Vector modes Scalar modes + first order constraint + 3 first order constraints

  39. Large momentum approximations

  40. Large momentum approximations

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